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Edge-coloring vertex-weightings of graphs
, 2021 Summary: Let \(G = (V (G), E(G))\) be a simple, finite and undirected graph of order \(n\). A \(k\)-vertex weighting of a graph \(G\) is a mapping \(w : V (G) \to \{1, \dots, k\}\). A \(k\)-vertex weighting induces an edge labeling \(f_w : E(G) \to \mathbb{N}\) such that \(f_w(uv) = w(u) + w(v)\). Such a labeling is called an edge-coloring \(k\)-vertex
Shiua, Wai Chee +2 more
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On Closed Modular Colorings of Trees
Discussiones Mathematicae Graph Theory, 2013 Two vertices u and v in a nontrivial connected graph G are twins if u and v have the same neighbors in V (G) − {u, v}. If u and v are adjacent, they are referred to as true twins; while if u and v are nonadjacent, they are false twins.
Phinezy Bryan, Zhang Ping
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Total dominator chromatic number of some operations on a graph
Bulletin of Computational Applied Mathematics, 2018 Let G be a simple graph. A total dominator coloring of G is a proper coloring of the vertices of G in which each vertex of the graph is adjacent to every vertex of some color class.
Nima Ghanbari, Saeid Alikhani
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THE LOCATING RAINBOW CONNECTION NUMBERS OF LOLLIPOP AND BARBELL GRAPHS
BarekengThe concept of the locating rainbow connection number of a graph is an innovation in graph coloring theory that combines the concepts of rainbow vertex coloring and partition dimension on graphs.
Ariestha Widyastuty Bustan +4 more
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The b$_q$-coloring of graphs [PDF]
Discrete Mathematics Letters, 2023 Brice Effantin
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Author Correction: Vertex coloring of graphs via phase dynamics of coupled oscillatory networks. [PDF]
Sci Rep, 2018 Parihar A +4 more
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Vertex coloring of graphs via phase dynamics of coupled oscillatory networks. [PDF]
Sci Rep, 2017 Parihar A +4 more
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Interval Vertex-Coloring of a Graph With Forbidden Colors
Discrete Mathematics, 1989 The classical model of coloring the vertices of a graph with single colors so that no two adjacent vertices are colored the same is too limited to be useful in many practical applications. Therefore one must consider more general notions of graph coloring and this article is devoted to one of such generalizations.
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Automatically generated algorithms for the vertex coloring problem. [PDF]
PLoS One, 2013 Contreras Bolton C, Gatica G, Parada V.
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Finite Vertex-Colored Ultrahomogeneous Oriented Graphs
A relational structure R is ultrahomogeneous if every isomorphism of finite induced substructures of R extends to an automorphism of R. We classify the ultrahomogeneous finite binary relational structures with one asymmetric binary relation and arbitrarily many unary relations.
Irene Heinrich +2 more
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